Navigation systems can use a variety of different sensors to detect changes to the motion and orientation of an object. For example accelerometers, gyros and magnetometers are often used. Accelerometers detect applied force, gyros detect rotation rates and magnetometers detect the Earth's magnetic field and so can be used to determine absolute orientation.
Inertial navigation systems, based on accelerometers and gyroscopes, can be used either on their own or together with other navigation systems such as GPS. Navigation/guidance of rockets and other munitions is often based on the use of micro-electro-mechanical (MEMS) sensors due to their small size and low-cost. The accuracy of these sensors is relatively poor and not sufficient to meet typical navigation requirements unless external sensors are used to estimate and correct the inertial sensor errors. Using additional aiding sensors in this way is the basis of what is known as ‘integrated navigation’.
Integrated navigation is usually based on an algorithmic technique known as Kalman Filtering, a process which blends data from the inertial sensors and external aiding sensors in an optimal way. For this technique to operate robustly, navigation errors must be maintained within certain limits at all times else the linearity assumptions on which the Kalman filter is founded will not be valid and the integrated navigation solution may become grossly inaccurate. It is desirable to avoid this situation by constraining navigation error growth during projectile flight.
When considering navigation Kalman filtering for applications involving rockets, missiles and other rotating platforms, initialising and maintaining an accurate roll (bank) angle presents the biggest challenge. An analysis of the problems associated with the use of inertial guidance technology in such applications is provided by J. S. Bird in “Inertial Sensor Performance Requirements for a Long Range Artillery Rocket” (DTIC ADA279936), with the conclusion that the roll gyro scale factor accuracy is critical and needs to be less than 5 parts-per-million (ppm).
Unfortunately, inexpensive low grade MEMS gyroscopes have a scale factor error of several thousand ppm. Using a gyroscope with a scale factor accuracy of less than 5 ppm would not be practical in terms of cost. Therefore there is a need for a system that can achieve the desired accuracy using inexpensive sensors with much lower scale factor accuracy.
The errors in gyroscope sensors are broadly divided into bias errors and scale factor errors. Although these and other errors are measured and removed as part of a factory calibration process, there will always be residual errors present when the sensors are actually used. These arise for a variety of reasons such as temperature and humidity changes, as well as other physical stresses affecting the unit. In general these errors may be different each time the unit is switched on.
As discussed in the above-referenced paper by J. S. Bird, in strapdown inertial navigation systems (i.e. those in which the inertial sensors are fixed to the body of the airframe as opposed to those in which the sensors are mounted on a gimballed platform that is free to rotate and so remain level at all times), one of the biggest problems comes from high roll rates. Typically roll rates for ballistic projectiles may be of the order of 10-20 full rotations per second, i.e. rotation rates of the order of a few thousand degrees per second. Therefore with a typical roll rate scale factor error of 1000 ppm, the roll angle (bank angle) calculated from this gyro would accumulate an error of a few degrees per second. For a typical projectile range of 30 to 60 km and a typical flight time of 1 to 2 minutes, this error quickly mounts up to be unacceptable.
Gyro bias error can readily be compensated immediately prior to use by averaging a series of readings while the gyro is known to be in a non-rotating state, e.g. prior to launch in the case of a projectile such as a rocket or missile. However, the scale factor error is rate-dependent and may not be measured and corrected whilst stationary. This suggests the need for a scale factor error correction process which operates in-flight, in a wholly self-contained fashion. This disclosure details such a process.
Alternative techniques which have been used in attempts to maintain roll accuracy include the use of non-inertial sensor aiding such as magnetometer, light sensor, GPS and/or thermopiles. These approaches add complexity and cost and introduce additional performance constraints. See for example “Attitude Determination with Magnetometers for un-Launched Munitions”, M. J. Wilson, DTIC ADA425992; and “On the Viability of Magnetometer-Based Projectile Orientation Measurements”, T. E. Harkins, DTIC ADA474475.
“Position Estimation for Projectiles Using Low-cost Sensors and Flight Dynamics” by L. D. Fairfax and F. E. Fresconi (DTIC ADA560811) describes another solution to this problem for gun-launched mortars which relies upon a multi-state Extended Kalman Filter to estimate position and velocity, but roll angle is determined via additional attitude aiding. This technique is applied to an application with a more benign roll rate profile than a typical artillery rocket.
U.S. Pat. No. 8,047,070 describes a process for estimating the roll angle of a gun-launched projectile. U.S. Pat. No. 8,047,070 uses body angular rate data as its measurements, as opposed to derived Euler angles. It also does not estimate or correct the roll rate scale factor error and it does not operate to preserve elevation and heading accuracy.